/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 + 2*x^2 + 4.

Traces:    [ 6, -6 ]
Density:   [ 0.0078229199, 0.99786259 ]
Numer max: [ 1, 24 ]
Numer av:  [ 0.0019557300, 2.4916727 ]
Denom max: [ 2, 98 ], [ [ <2, 1> ], [ <2, 1>, <7, 2> ] ]
Denom LCM: [ 2, 98 ], [ [ <2, 1> ], [ <2, 1>, <7, 2> ] ]
*/

G := PermutationGroup(ATLASGroup("3ON"));
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 342, 342, [
    <1, 133, -1>, <1, 136, 1/2*w^3>,  <2, 134, 1>, <2, 136, 1>, <2, 137, 
    -1/2*w^3>,  <3, 136, -1>,  <4, 133, -1/2*w^3>, <4, 135, -1>, <4, 136, 1>,  
    <5, 133, -1>, <5, 136, 1/2*w^3>, <5, 137, -1>, <5, 138, 1>,  <6, 136, 
    1/2*w^3>, <6, 137, -1>,  <7, 7, -1/2*w^3>, <7, 8, -1>, <7, 9, -1>, <7, 11, 
    1/2*w^3>,  <8, 9, -1/2*w^3>, <8, 10, -1/2*w^3>, <8, 11, 1>, <8, 12, -1>,  
    <9, 7, 1>, <9, 9, 1/2*w^3>, <9, 11, -1>, <9, 12, 1>,  <10, 7, -1>, <10, 8, 
    -1/2*w^3>, <10, 9, -1/2*w^3>, <10, 11, 1>,  <11, 8, -1>, <11, 9, -1>, <11, 
    10, -1>, <11, 11, 1/2*w^3>,  <12, 9, -1>, <12, 10, -1>, <12, 11, 1/2*w^3>, 
    <12, 12, -1/2*w^3>,  <13, 173, 1>, <13, 174, -1>,  <14, 170, -1>, <14, 172, 
    -1>, <14, 173, 1/2*w^3>,  <15, 170, 1>, <15, 173, -1/2*w^3>,  <16, 171, -1>,
    <16, 172, -1>, <16, 173, 1/2*w^3>, <16, 174, -1/2*w^3>,  <17, 169, 1>, <17, 
    172, -1/2*w^3>, <17, 173, 1>, <17, 174, -1>,  <18, 170, -1/2*w^3>, <18, 173,
    1>,  <19, 230, 1/2*w^3>, <19, 234, -1>,  <20, 230, 1>, <20, 232, 1>, <20, 
    233, -1/2*w^3>,  <21, 230, -1>,  <22, 230, 1>, <22, 231, -1>, <22, 234, 
    -1/2*w^3>,  <23, 229, 1>, <23, 230, 1/2*w^3>, <23, 233, -1>, <23, 234, -1>, 
    <24, 230, 1/2*w^3>, <24, 233, -1>,  <25, 151, -1/2*w^3>, <25, 154, 1>,  <26,
    153, 1/2*w^3>, <26, 154, 1/2*w^3>, <26, 155, -1>, <26, 156, 1>,  <27, 151, 
    1>, <27, 154, -1/2*w^3>, <27, 155, 1>,  <28, 151, -1>, <28, 154, 1/2*w^3>,  
    <29, 153, 1>, <29, 154, 1>,  <30, 152, 1>, <30, 153, 1>, <30, 154, 1>, <30, 
    155, -1/2*w^3>,  <31, 191, -1>,  <32, 189, -1>, <32, 190, -1>,  <33, 190, 
    1>,  <34, 188, 1>, <34, 191, -1/2*w^3>,  <35, 191, -1>, <35, 192, 1>,  <36, 
    187, 1>, <36, 190, -1/2*w^3>,  <37, 62, -1>, <37, 63, -1>, <37, 64, -1>, 
    <37, 65, 1/2*w^3>,  <38, 65, 1>,  <39, 62, 1/2*w^3>, <39, 65, -1>, <39, 66, 
    -1>,  <40, 61, 1>, <40, 64, -1/2*w^3>, <40, 65, 1>,  <41, 64, -1>, <41, 65, 
    1/2*w^3>,  <42, 62, -1>, <42, 65, 1/2*w^3>,  <43, 127, -1/2*w^3>, <43, 128, 
    -1>, <43, 129, -1>, <43, 131, 1/2*w^3>,  <44, 129, -1/2*w^3>, <44, 130, 
    -1/2*w^3>, <44, 131, 1>, <44, 132, -1>,  <45, 127, 1>, <45, 129, 1/2*w^3>, 
    <45, 131, -1>, <45, 132, 1>,  <46, 127, -1>, <46, 128, -1/2*w^3>, <46, 129, 
    -1/2*w^3>, <46, 131, 1>,  <47, 128, -1>, <47, 129, -1>, <47, 130, -1>, <47, 
    131, 1/2*w^3>,  <48, 129, -1>, <48, 130, -1>, <48, 131, 1/2*w^3>, <48, 132, 
    -1/2*w^3>,  <49, 326, -1>, <49, 328, 1>,  <50, 330, -1>,  <51, 325, -1>, 
    <51, 330, 1>,  <52, 326, -1/2*w^3>, <52, 329, 1>,  <53, 326, -1>,  <54, 327,
    -1>, <54, 330, -1/2*w^3>,  <55, 218, 1/2*w^3>, <55, 221, -1>,  <56, 218, 1>,
    <56, 219, -1>, <56, 222, -1/2*w^3>,  <57, 218, -1>,  <58, 218, 1>, <58, 220,
    1>, <58, 221, -1/2*w^3>,  <59, 217, 1>, <59, 218, 1/2*w^3>, <59, 221, -1>, 
    <59, 222, -1>,  <60, 218, 1/2*w^3>, <60, 222, -1>,  <61, 38, 1>, <61, 40, 
    1>, <61, 41, -1/2*w^3>,  <62, 38, 1/2*w^3>, <62, 42, -1>,  <63, 37, -1>, 
    <63, 38, -1/2*w^3>, <63, 41, 1>, <63, 42, 1>,  <64, 38, 1/2*w^3>, <64, 41, 
    -1>,  <65, 38, 1>,  <66, 38, 1>, <66, 39, -1>, <66, 42, -1/2*w^3>,  <67, 
    147, 1/2*w^3>, <67, 148, 1/2*w^3>, <67, 149, -1>, <67, 150, 1>,  <68, 145, 
    -1/2*w^3>, <68, 148, 1>,  <69, 147, -1>, <69, 148, -1>,  <70, 146, 1>, <70, 
    147, 1>, <70, 148, 1>, <70, 149, -1/2*w^3>,  <71, 145, -1>, <71, 148, 
    1/2*w^3>, <71, 149, -1>,  <72, 145, -1>, <72, 148, 1/2*w^3>,  <73, 285, 
    -1/2*w^3>, <73, 288, -1>,  <74, 283, -1/2*w^3>, <74, 284, -1>, <74, 285, 
    -1>, <74, 286, 1>,  <75, 285, 1>, <75, 288, 1/2*w^3>,  <76, 284, -1>, <76, 
    285, -1>,  <77, 283, -1>, <77, 284, -1/2*w^3>, <77, 285, -1/2*w^3>, <77, 
    287, 1>,  <78, 283, -1>, <78, 285, -1/2*w^3>, <78, 288, -1>,  <79, 337, 
    1/2*w^3>, <79, 340, -1>,  <80, 337, 1>, <80, 339, 1/2*w^3>, <80, 341, -1>, 
    <80, 342, 1>,  <81, 337, -1>, <81, 340, 1/2*w^3>,  <82, 337, 1>, <82, 341, 
    -1>,  <83, 337, 1/2*w^3>, <83, 338, 1>, <83, 339, 1>, <83, 341, -1/2*w^3>,  
    <84, 337, 1/2*w^3>, <84, 339, 1>, <84, 340, -1>,  <85, 86, 1>,  <86, 85, 1>,
    <87, 89, -1>,  <88, 90, 1>,  <89, 87, -1>,  <90, 88, 1>,  <91, 235, 
    -1/2*w^3>, <91, 236, -1>, <91, 237, -1>, <91, 238, 1>,  <92, 238, 1/2*w^3>, 
    <92, 239, -1>,  <93, 235, 1>, <93, 236, 1/2*w^3>, <93, 238, -1/2*w^3>, <93, 
    240, -1>,  <94, 235, -1>, <94, 238, 1/2*w^3>, <94, 239, -1>,  <95, 238, 1>, 
    <95, 239, -1/2*w^3>,  <96, 236, -1>, <96, 238, 1>,  <97, 205, -1>, <97, 208,
    1/2*w^3>,  <98, 206, 1>, <98, 207, 1>, <98, 208, 1>, <98, 209, -1/2*w^3>,  
    <99, 207, -1>, <99, 208, -1>,  <100, 205, -1/2*w^3>, <100, 208, 1>,  <101, 
    205, -1>, <101, 208, 1/2*w^3>, <101, 209, -1>,  <102, 207, 1/2*w^3>, <102, 
    208, 1/2*w^3>, <102, 209, -1>, <102, 210, 1>,  <103, 105, -1>, <103, 106, 
    -1>, <103, 107, 1/2*w^3>, <103, 108, -1/2*w^3>,  <104, 104, -1/2*w^3>, <104,
    107, 1>,  <105, 103, -1>, <105, 106, 1/2*w^3>, <105, 107, -1>, <105, 108, 
    1>,  <106, 107, 1>, <106, 108, -1>,  <107, 104, -1>, <107, 107, 1/2*w^3>,  
    <108, 104, -1>, <108, 106, -1>, <108, 107, 1/2*w^3>,  <109, 181, 1>, <109, 
    183, 1/2*w^3>, <109, 185, -1>, <109, 186, 1>,  <110, 182, -1>, <110, 186, 
    1/2*w^3>,  <111, 182, 1>, <111, 183, -1>, <111, 186, -1/2*w^3>,  <112, 183, 
    1>, <112, 184, 1>, <112, 185, -1/2*w^3>, <112, 186, 1/2*w^3>,  <113, 185, 
    -1>, <113, 186, 1>,  <114, 182, -1/2*w^3>, <114, 186, 1>,  <115, 212, 1>, 
    <115, 216, -1/2*w^3>,  <116, 211, 1>, <116, 212, 1/2*w^3>, <116, 213, 
    1/2*w^3>, <116, 215, -1>,  <117, 212, -1/2*w^3>, <117, 216, 1>,  <118, 212, 
    1/2*w^3>, <118, 215, -1>, <118, 216, -1>,  <119, 212, 1>, <119, 213, 1>, 
    <119, 214, 1>, <119, 215, -1/2*w^3>,  <120, 212, 1>, <120, 213, 1>,  <121, 
    295, 1>, <121, 297, 1/2*w^3>,  <122, 295, 1/2*w^3>, <122, 296, 1>, <122, 
    298, -1>, <122, 300, -1/2*w^3>,  <123, 295, -1/2*w^3>, <123, 297, -1>, <123,
    298, 1>,  <124, 295, 1/2*w^3>, <124, 297, 1>,  <125, 295, 1>, <125, 300, 
    -1>,  <126, 295, 1>, <126, 298, -1/2*w^3>, <126, 299, 1>, <126, 300, -1>,  
    <127, 43, -1/2*w^3>, <127, 44, -1>, <127, 45, -1>, <127, 47, 1/2*w^3>,  
    <128, 45, -1/2*w^3>, <128, 46, -1/2*w^3>, <128, 47, 1>, <128, 48, -1>,  
    <129, 43, 1>, <129, 45, 1/2*w^3>, <129, 47, -1>, <129, 48, 1>,  <130, 43, 
    -1>, <130, 44, -1/2*w^3>, <130, 45, -1/2*w^3>, <130, 47, 1>,  <131, 44, -1>,
    <131, 45, -1>, <131, 46, -1>, <131, 47, 1/2*w^3>,  <132, 45, -1>, <132, 46, 
    -1>, <132, 47, 1/2*w^3>, <132, 48, -1/2*w^3>,  <133, 1, -1>, <133, 3, 
    -1/2*w^3>,  <134, 2, 1>, <134, 3, -1>, <134, 6, -1/2*w^3>,  <135, 1, 
    1/2*w^3>, <135, 3, 1>, <135, 4, -1>,  <136, 3, -1>,  <137, 3, -1/2*w^3>, 
    <137, 6, -1>,  <138, 1, -1>, <138, 3, -1/2*w^3>, <138, 5, 1>, <138, 6, -1>, 
    <139, 140, -1>, <139, 142, -1>, <139, 143, 1/2*w^3>,  <140, 139, -1>, <140, 
    143, 1>,  <141, 139, 1>, <141, 140, 1/2*w^3>, <141, 143, -1>, <141, 144, 
    -1>,  <142, 142, -1/2*w^3>, <142, 143, 1>,  <143, 142, -1>, <143, 143, 
    1/2*w^3>,  <144, 139, -1/2*w^3>, <144, 140, -1>, <144, 141, -1>, <144, 143, 
    1/2*w^3>,  <145, 68, -1/2*w^3>, <145, 72, 1>,  <146, 69, 1>, <146, 70, 1>, 
    <146, 71, -1/2*w^3>, <146, 72, 1/2*w^3>,  <147, 68, 1>, <147, 69, -1>, <147,
    72, -1/2*w^3>,  <148, 68, -1>, <148, 72, 1/2*w^3>,  <149, 71, -1>, <149, 72,
    1>,  <150, 67, 1>, <150, 69, 1/2*w^3>, <150, 71, -1>, <150, 72, 1>,  <151, 
    25, -1/2*w^3>, <151, 28, 1>,  <152, 27, 1/2*w^3>, <152, 28, 1/2*w^3>, <152, 
    29, -1>, <152, 30, 1>,  <153, 25, 1>, <153, 28, -1/2*w^3>, <153, 29, 1>,  
    <154, 25, -1>, <154, 28, 1/2*w^3>,  <155, 27, 1>, <155, 28, 1>,  <156, 26, 
    1>, <156, 27, 1>, <156, 28, 1>, <156, 29, -1/2*w^3>,  <157, 224, -1>, <157, 
    228, 1/2*w^3>,  <158, 223, 1>, <158, 225, 1/2*w^3>, <158, 228, 1>,  <159, 
    224, 1/2*w^3>, <159, 227, -1>, <159, 228, -1>,  <160, 228, 1>,  <161, 225, 
    1>, <161, 228, 1/2*w^3>,  <162, 224, -1>, <162, 225, 1>, <162, 226, 1>, 
    <162, 228, 1/2*w^3>,  <163, 247, 1/2*w^3>, <163, 250, -1>,  <164, 247, 1>, 
    <164, 249, 1/2*w^3>, <164, 252, 1>,  <165, 247, -1>, <165, 250, 1/2*w^3>, 
    <165, 251, -1>,  <166, 247, 1>,  <167, 247, 1/2*w^3>, <167, 249, 1>,  <168, 
    247, 1/2*w^3>, <168, 248, 1>, <168, 249, 1>, <168, 250, -1>,  <169, 13, -1>,
    <169, 14, -1/2*w^3>, <169, 15, -1/2*w^3>, <169, 17, 1>,  <170, 15, -1>, 
    <170, 18, -1/2*w^3>,  <171, 13, 1/2*w^3>, <171, 14, 1>, <171, 15, 1>, <171, 
    16, -1>,  <172, 14, -1>, <172, 15, -1>,  <173, 15, -1/2*w^3>, <173, 18, -1>,
    <174, 13, -1>, <174, 15, -1/2*w^3>, <174, 18, -1>,  <175, 242, -1>, <175, 
    243, -1>,  <176, 241, -1>, <176, 243, -1/2*w^3>, <176, 246, -1>,  <177, 241,
    1>, <177, 242, 1/2*w^3>, <177, 243, 1/2*w^3>, <177, 245, -1>,  <178, 243, 
    -1/2*w^3>, <178, 246, -1>,  <179, 243, -1>, <179, 246, -1/2*w^3>,  <180, 
    241, -1/2*w^3>, <180, 242, -1>, <180, 243, -1>, <180, 244, 1>,  <181, 109, 
    1>, <181, 110, 1/2*w^3>, <181, 111, 1/2*w^3>, <181, 113, -1>,  <182, 110, 
    1>, <182, 114, -1/2*w^3>,  <183, 110, -1>, <183, 111, -1>,  <184, 110, 1>, 
    <184, 111, 1>, <184, 112, 1>, <184, 113, -1/2*w^3>,  <185, 110, 1/2*w^3>, 
    <185, 113, -1>, <185, 114, -1>,  <186, 110, 1/2*w^3>, <186, 114, -1>,  <187,
    33, 1/2*w^3>, <187, 36, 1>,  <188, 31, -1/2*w^3>, <188, 34, 1>,  <189, 32, 
    -1>, <189, 33, -1>,  <190, 33, 1>,  <191, 31, -1>,  <192, 31, -1>, <192, 35,
    1>,  <193, 193, 1>,  <194, 194, 1>,  <195, 195, 1>,  <196, 196, 1>,  <197, 
    197, 1>,  <198, 198, 1>,  <199, 314, 1>, <199, 315, 1>, <199, 316, 1>, <199,
    317, -1/2*w^3>,  <200, 314, 1/2*w^3>, <200, 318, -1>,  <201, 314, -1/2*w^3>,
    <201, 317, 1>, <201, 318, 1>,  <202, 313, 1>, <202, 314, 1/2*w^3>, <202, 
    315, 1/2*w^3>, <202, 317, -1>,  <203, 314, 1>, <203, 315, 1>,  <204, 314, 
    1>, <204, 318, -1/2*w^3>,  <205, 97, 1>, <205, 100, -1/2*w^3>,  <206, 97, 
    1/2*w^3>, <206, 98, 1>, <206, 99, 1>, <206, 101, -1/2*w^3>,  <207, 97, 
    -1/2*w^3>, <207, 99, -1>, <207, 100, 1>,  <208, 97, 1/2*w^3>, <208, 100, 
    -1>,  <209, 97, 1>, <209, 101, -1>,  <210, 97, 1>, <210, 99, 1/2*w^3>, <210,
    101, -1>, <210, 102, 1>,  <211, 116, 1>, <211, 117, -1>, <211, 118, -1>, 
    <211, 120, -1/2*w^3>,  <212, 115, -1>, <212, 117, -1/2*w^3>,  <213, 115, 1>,
    <213, 117, 1/2*w^3>, <213, 120, 1>,  <214, 117, -1/2*w^3>, <214, 118, 
    -1/2*w^3>, <214, 119, 1>, <214, 120, -1>,  <215, 117, -1>, <215, 118, -1>,  
    <216, 115, -1/2*w^3>, <216, 117, -1>,  <217, 55, -1>, <217, 57, -1/2*w^3>, 
    <217, 59, 1>, <217, 60, -1>,  <218, 57, -1>,  <219, 56, -1>, <219, 57, 1>, 
    <219, 60, 1/2*w^3>,  <220, 55, -1/2*w^3>, <220, 57, -1>, <220, 58, 1>,  
    <221, 55, -1>, <221, 57, -1/2*w^3>,  <222, 57, -1/2*w^3>, <222, 60, -1>,  
    <223, 158, 1>, <223, 160, 1>, <223, 161, -1/2*w^3>,  <224, 157, -1>, <224, 
    160, 1/2*w^3>,  <225, 160, -1/2*w^3>, <225, 161, 1>,  <226, 157, -1>, <226, 
    160, 1/2*w^3>, <226, 161, -1>, <226, 162, 1>,  <227, 157, -1/2*w^3>, <227, 
    159, -1>, <227, 160, 1>,  <228, 160, 1>,  <229, 19, -1>, <229, 21, 
    -1/2*w^3>, <229, 23, 1>, <229, 24, -1>,  <230, 21, -1>,  <231, 19, 1/2*w^3>,
    <231, 21, 1>, <231, 22, -1>,  <232, 20, 1>, <232, 21, -1>, <232, 24, 
    -1/2*w^3>,  <233, 21, -1/2*w^3>, <233, 24, -1>,  <234, 19, -1>, <234, 21, 
    -1/2*w^3>,  <235, 92, 1>, <235, 94, -1>,  <236, 92, 1/2*w^3>, <236, 95, -1>,
    <236, 96, -1>,  <237, 91, -1>, <237, 92, -1/2*w^3>, <237, 94, 1/2*w^3>, 
    <237, 96, 1>,  <238, 92, 1/2*w^3>, <238, 95, -1>,  <239, 92, 1>, <239, 95, 
    -1/2*w^3>,  <240, 92, 1>, <240, 93, -1>, <240, 94, -1>, <240, 96, -1/2*w^3>,
    <241, 176, -1>, <241, 178, 1>,  <242, 175, -1>, <242, 178, 1/2*w^3>, <242, 
    179, -1>,  <243, 178, -1/2*w^3>, <243, 179, 1>,  <244, 175, -1>, <244, 176, 
    -1/2*w^3>, <244, 178, 1/2*w^3>, <244, 180, 1>,  <245, 175, -1/2*w^3>, <245, 
    176, -1>, <245, 177, -1>, <245, 178, 1>,  <246, 178, 1>, <246, 179, 
    -1/2*w^3>,  <247, 166, 1>,  <248, 163, -1>, <248, 166, 1/2*w^3>, <248, 167, 
    -1>, <248, 168, 1>,  <249, 166, -1/2*w^3>, <249, 167, 1>,  <250, 163, -1>, 
    <250, 166, 1/2*w^3>,  <251, 163, -1/2*w^3>, <251, 165, -1>, <251, 166, 1>,  
    <252, 164, 1>, <252, 166, 1>, <252, 167, -1/2*w^3>,  <253, 254, -1>, <253, 
    255, 1>, <253, 258, 1/2*w^3>,  <254, 253, -1>, <254, 258, 1>,  <255, 255, 
    -1/2*w^3>, <255, 258, -1>,  <256, 253, -1>, <256, 254, -1/2*w^3>, <256, 257,
    1>, <256, 258, 1>,  <257, 253, -1/2*w^3>, <257, 254, -1>, <257, 256, 1>, 
    <257, 258, 1/2*w^3>,  <258, 255, 1>, <258, 258, 1/2*w^3>,  <259, 272, -1>, 
    <259, 273, 1>, <259, 276, 1/2*w^3>,  <260, 275, -1>, <260, 276, 1>,  <261, 
    271, -1>, <261, 273, -1/2*w^3>, <261, 275, 1>, <261, 276, -1>,  <262, 272, 
    -1/2*w^3>, <262, 276, 1>,  <263, 272, -1>, <263, 276, 1/2*w^3>,  <264, 273, 
    1>, <264, 274, 1>, <264, 275, -1/2*w^3>, <264, 276, 1/2*w^3>,  <265, 265, 
    1/2*w^3>, <265, 266, 1>, <265, 267, 1>, <265, 268, -1>,  <266, 265, 1>, 
    <266, 266, 1/2*w^3>, <266, 269, -1>, <266, 270, -1>,  <267, 265, -1>, <267, 
    266, -1/2*w^3>, <267, 267, -1/2*w^3>, <267, 269, 1>,  <268, 265, 1>, <268, 
    266, 1/2*w^3>, <268, 268, -1/2*w^3>, <268, 270, -1>,  <269, 265, 1/2*w^3>, 
    <269, 266, 1>, <269, 268, -1>, <269, 270, -1/2*w^3>,  <270, 265, 1/2*w^3>, 
    <270, 266, 1>, <270, 267, 1>, <270, 269, -1/2*w^3>,  <271, 259, -1/2*w^3>, 
    <271, 260, -1>, <271, 261, -1>, <271, 263, 1/2*w^3>,  <272, 262, -1/2*w^3>, 
    <272, 263, 1>,  <273, 259, 1>, <273, 263, -1>,  <274, 259, -1>, <274, 260, 
    -1/2*w^3>, <274, 263, 1>, <274, 264, 1>,  <275, 260, -1>, <275, 262, -1>, 
    <275, 263, 1/2*w^3>,  <276, 262, -1>, <276, 263, 1/2*w^3>,  <277, 308, 1>, 
    <277, 310, 1>, <277, 311, -1/2*w^3>,  <278, 308, 1/2*w^3>, <278, 312, -1>,  
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        ] ])
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [4, 0, 2, 0, 1])> where K is 
RationalField();
K<w>:=BaseRing(M);
K;
M;
